SPTRFS(3)

💅 SPTRFS (3) — sptrfs.f

okay so we're in the sptrfs.f(3) page, which lives under the Library Functions Manual umbrella — welcome to the LAPACK corner of the universe, bestie 🫶

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sptrfs.f

(yes, that's the whole name, it's giving "full government name on the birth certificate" energy 😭 that's literally just where the source file lives, don't panic)

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine SPTRFS (n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr,
    work, info)

SPTRFS — that's her, that's the main character 💫

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🎀 Function/Subroutine Documentation 🎀

subroutine SPTRFS (integer n, integer nrhs, real, dimension( * ) d, real,
    dimension( * ) e, real, dimension( * ) df, real, dimension( * ) ef,
    real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x,
    integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real,
    dimension( * ) work, integer info)

SPTRFS 🔥

💜 Purpose 💜

!> SPTRFS improves the computed solution to a system of linear !> equations when the coefficient matrix is symmetric positive definite !> and tridiagonal, and provides error bounds and backward error !> estimates for the solution.

so basically: you already have a solution (from SPTTRS, keep reading bestie) and it's a little crunchy around the edges — SPTRFS comes in and polishes it ✨ and then hands you receipts on how wrong it could possibly be, in both directions. symmetric positive definite AND tridiagonal? she's picky, but she slays. no cap.

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🦋 Parameters 🦋

• N

!> N is INTEGER !> The order of the matrix A. N >= 0.

the size of the whole situation, aka the order of matrix A. bestie said N >= 0 and she meant it 🙏

• NRHS

!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0.

how many right hand sides we're serving, i.e., how many columns matrix B has. NRHS >= 0, periodt 💅

• D

!> D is REAL array, dimension (N) !> The n diagonal elements of the tridiagonal matrix A.

REAL array, dimension (N). the n diagonal elements of the tridiagonal matrix A — the main character of the tridiagonal trio 👑

• E

!> E is REAL array, dimension (N-1) !> The (n-1) subdiagonal elements of the tridiagonal matrix A.

REAL array, dimension (N-1) — note the N-1, she's one shorter, she's the quirky sidekick. the (n-1) subdiagonal elements of the tridiagonal matrix A 🦋

• DF

!> DF is REAL array, dimension (N) !> The n diagonal elements of the diagonal matrix D from the !> factorization computed by SPTTRF.

REAL array, dimension (N). the n diagonal elements of the diagonal matrix D from the factorization computed by SPTTRF — yes, D and DF, they're different things, don't @ me 🙈

• EF

!> EF is REAL array, dimension (N-1) !> The (n-1) subdiagonal elements of the unit bidiagonal factor !> L from the factorization computed by SPTTRF.

REAL array, dimension (N-1). the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by SPTTRF ⭐

• B

!> B is REAL array, dimension (LDB,NRHS) !> The right hand side matrix B.

REAL array, dimension (LDB,NRHS) — the right hand side matrix B. your input, your problem, your moment 💀

• LDB

!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N).

INTEGER. leading dimension of the array B. LDB >= max(1,N) — remember the max(1,N), it's important iykyk

• X

!> X is REAL array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by SPTTRS. !> On exit, the improved solution matrix X.

REAL array, dimension (LDX,NRHS). this one's a glow-up arc: on entry it's the solution matrix X as computed by SPTTRS, and on exit it's the improved solution matrix X 🧚✨ she went to the salon and came back better

• LDX

!> LDX is INTEGER !> The leading dimension of the array X. LDX >= max(1,N).

INTEGER. leading dimension of the array X. LDX >= max(1,N) 🫶

• FERR

!> FERR is REAL array, dimension (NRHS) !> The forward error bound for each solution vector !> X(j) (the j-th column of the solution matrix X). !> If XTRUE is the true solution corresponding to X(j), FERR(j) !> is an estimated upper bound for the magnitude of the largest !> element in (X(j) - XTRUE) divided by the magnitude of the !> largest element in X(j).

REAL array, dimension (NRHS). the forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). if XTRUE is the true solution corresponding to X(j), then FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). it's giving "how far off am i, realistically" 🔥

• BERR

!> BERR is REAL array, dimension (NRHS) !> The componentwise relative backward error of each solution !> vector X(j) (i.e., the smallest relative change in !> any element of A or B that makes X(j) an exact solution).

REAL array, dimension (NRHS). the componentwise relative backward error of each solution vector X(j) — i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution. "how much would i have to lie to be right" 😭 iconic

• WORK

!> WORK is REAL array, dimension (2*N)

REAL array, dimension (2*N). that's it. that's the whole description. she doesn't owe you an explanation 💅

• INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value

INTEGER, our beloved status report:

• = 0: successful exit 🎉 slay
• < 0: if INFO = -i, the i-th argument had an illegal value. not me passing a bad argument 💀

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🌈 Internal Parameters 🌈

!> ITMAX is the maximum number of steps of iterative refinement.

ITMAX is the maximum number of steps of iterative refinement. she's internal, she's not on the menu, but now you know her name 🧚

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

the whole squad showed up, we love a collaborative effort 🫶💖

Definition at line 161 of file sptrfs.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. (the robot did this one, not a human, respect the automation 🤖✨)

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heads up bestie: FERR and BERR are estimates and bounds, not certified truths — that's literally what the manpage says, so don't come for me 🫶

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